Turbine vane cooling improves component life. Vane platforms may be externally impingement cooled, as shown in FIG. 2, in which a cooling air flow 919 is directed to the plenum 916, thereby convectively cooling the outer surface 918 of the vane platform 915. It is also known to cool turbine vane platforms by film cooling, as shown in FIGS. 3a and 3b, and described in U.S. Pat. No. 5,417,545. A plurality of regularly-spaced cooling holes 922 in the platform 915, upstream of the airfoils 912, permit a cooling airflow to enter the gas path 917 and form a uniform film or blanket 924 of cool air on the vane platform in an attempt to insulate it from the hot gases. However, the solution of U.S. Pat. No. 5,417,545 is susceptible to the limited cooling ability of the thin air film in the face of the extreme temperatures, turbulence and varied temperature distribution of the combustion gases. Accordingly, improvements to the art are needed.